is it safe and reliable to have a stage2 exedy clutch with a stock flywheel?

 

As long as the flywheel is considered safe, an uprated clutch should be fine. I would highly recommend a lightweight unit, having had two such combinations on my own cars.

 

Isn't the stock flywheel stronger than most of the aftermarket ones anyways?

 

Heavier doesn't necessarily mean stronger. The weight of a stock flywheel is generally there to help driveability, even though it hurts acceleration and potentially the fuel mileage. Most of the reputable manufacturers of flywheels use very high-grade materials and processes to make certain that the product is at least as strong as the OE part. In the case of Exedy, which makes many, if not all, stock Subaru clutches, the OE flywheel might be made in a factory next to their lightweight flywheel models.